Number of standard Young tableaux with n cells and 3 as last value in the first row.

Terms

a(0) =2a(1) =3a(2) =5a(3) =10a(4) =19a(5) =41a(6) =86a(7) =197a(8) =449a(9) =1087a(10) =2650a(11) =6722a(12) =17227a(13) =45267a(14) =120069a(15) =323442a(16) =877777a(17) =2405399a(18) =6628760a(19) =18384040a(20) =51204735a(21) =143252991a(22) =402115301a(23) =1132464571a(24) =3197928097a(25) =9053803101a(26) =25689876776a(27) =73047889402a(28) =208100836969a(29) =593897902349